COTES, ROGER, born July 10, 16S2, at Burbage, near Leicester, of which placo his father was rector. His first education was received partly at Leicester school, partly from an uncle, who was the father of Dr. Robert Smith, the author of the Optics.' He was afterwards placed at Sr. Paul's School, and in April 1699 was admitted at Trinity College, Cambridge, of which foundation ho was elected fellow in 1705. In January 1706 he was elected Plumian Professor, at the time of the establishment of that chair. In 1713 he took orders, lie died June 5, 1716, aged 34, and was buried in the chapel of his college, where there is an epitaph upon him by Dr. Bentley. Ile was succeeded in the Plumian professorship by his cousin, Dr. R. Smith, the editor of his works. (' Bioeraplaia Britaonica2) The early death of Cotes being taken into account, few persons have left more reputation behind them than he di i in matters of exact science. Newton is reported to have said, "If Cotes had lived, we should have known something." As it is, we have not much to say in a biographical article. The discoveries of Cotes have exercised a decided influence upon various parts of mathematics. For hia repu tation on the continent, it is unfortunate that he died so near the termination of the discussion relative to fluxion. The problems which ho left were made the subject of a challenge to foreign mathematicians by Dr. Brook Taylor, In the interval which elapsed between his death and the publication of his works; and some bitterness of f, ding was excited which was unfavourable to the proper estimation of their merits. (Montucla, 'Hist. dee Math.,' vol. p. 151.) We shall now briefly describe them.
The first work which Cotes published was the second edition of Newton's Principle' (1713), to which he prefixed the well-known preface. This treats of gravitation in general, and of the objections
which were made to it. He also published an account of a remarkable meteor in the' l'hil. Trans.' for 1715. His hydrostatical and pneuma tical lectures were printed after his death, in 1738, by Dr. It. Smith.
The mathematical papers of Cotes were published after his death by Dr. Smith, tinder the title of 'Harmonia Mensurarum, eive analysis et synthesis per rationum et angulornm mensnras promote, : accedunt alia opnscula mathematics,' Cambridge, 1722. Tho most definite description which can be given of it is, that it was the earliest work in which decided progress was made In the application of logarithms And of the properties of the circle, to the calculus of fluents. The first book contams an extended comparison of systems of logarithms, with applications of then to the finding of areas. The second is what we ahoul'I now call a table of integrals, depending on logarithms and arcs of a circle. The third consists in applications of the second. Then follows a mass of extensions, digested, mostly from Cotcs's papers, by Dr. Smith. The opiescuta consist in-1. A tract on the estimation of errors in mixed mathematics, consisting mostly of an investigation of the method of choosing spherical triangles, so that the errors of the data shall produce least effect upon the qucesita, but ending with what we must call the first glimpse of a method of choosing the proper mean for discordant observations. 2. A tract on the differential method of Newton. 3. On the construction of tables by differences. 4. On the descent of heavy bodies ; on cycloidal motion, &e.